'It hurts', says Buttler as champions England crash out
England were defeated by 33 run by arch-rivals Australia on Saturday to suffer a sixth loss in seven games at the tournament.
"It certainly feels like a low point. I've had a few but definitely as a captain," admitted a crestfallen Buttler.
"To be stood in this position having arrived in India with high hopes is incredibly tough and disappointing. It hurts a lot."
Australia had been bowled out for 286 but still had enough firepower to dismiss England for 253 as the defending champions remain bottom of the table and still with two games to play.
"We are disappointed. I feel like we are having the same chat after every game at the minute," added Buttler.
"We haven't done ourselves justice. Coming into the tournament we fancied ourselves to have a real go and push whoever it was going to be all the way."
He added: "We've let ourselves down. We've let down people down at home, who support us through thick and thin and we wear that on our own shoulders."
Australia are well set to make the semi-finals, sitting third in the standings with 10 points after a fifth win in succession followed two opening losses.
"It's been great. The boys have played brilliantly, every game we've found a way to win," said skipper Pat Cummins.
"I feel like every game we've improved a little bit. I still don't think we've played the complete game."